Solve for $x$ and $y$ using elimination. $\begin{align*}-7x-2y &= -3 \\ -2x-y &= 6\end{align*}$
We can eliminate $y$ when its corresponding coefficients are negative inverses. Recalling our knowledge of least common multiples, multiply the top equation by $-1$ and the bottom equation by $2$ $\begin{align*}7x+2y &= 3\\ -4x-2y &= 12\end{align*}$ Add the top and bottom equations. $3x = 15$ Divide both sides by $3$ and reduce as necessary. $x = 5$ Substitute $5$ for $x$ in the top equation. $-7( 5)-2y = -3$ $-35-2y = -3$ $-2y = 32$ $y = -16$ The solution is $\enspace x = 5, \enspace y = -16$.